This formula is valid for all thermodynamic system considered as canonical ensemble and it is also valid for black holes. \(S_{0}\)  denotes the black hole entropy and thus we can replace \(T \rightarrow T_{H}\) . Now, we can determine \(S_{0}^{^{\prime \prime }}\) . We consider the entropy, which is suggested in Ref. [1]} and based on Ref. [2]}, has the form,
\(S=x\beta ^{m}+y\beta ^{-n}\, ,\) 
